Efficient single-hop directional multichannel system

ABSTRACT

A shared directional multichannel for efficiently transmitting k=( log p  n   choose (p-1) concurrent, non-interfering transmissions from a set of m≧k source stations, each having p transmitters, to a set of n destination stations, each having one receiver, without active repeater components. The multichannel architecture permits implementation of an efficient single-hop multichannel system using optical star couplers in a manner that limits the power spreading loss to the n/p value known for bus-oriented networks instead of n 2  /p. Several coupling stages are employed, each stage having a plurality of identical substantially-square directional couplers, to obtain channel concurrency k, which is an improvement over the concurrency p available in bus-oriented networks, without the higher power spreading loss normally arising from the larger number of connections between each source station and every destination station.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to single-hop multichannel communicationnetworks in general, and more specifically, to a power-efficient,non-bus-oriented single-hop interconnect network architecture foroptical signals.

2. Discussion of the Related Art

The evolution of modern data communications networks has steadilyincreased the demand for networks offering high data transmission speedsand high levels of data parallelism or channel concurrency. Datatransmission rates are limited by the physical technology composing thenetwork interconnection linkages. Channel concurrency is limited by therequirement that multiple transmissions remain distinguishable withinthe network when routed to the appropriate destinations. With standardbus-oriented network architectures, the number of concurrenttransmissions is less than or equal to the number of buses.

A bus is a device used to completely interconnect a set of transmittersto a set of receivers. A network is said to be bus-oriented if allconnections are made by buses and each transmitter and receiver is ononly one bus. Optimal concurrency requires a protocol for transmittingdata packets through a network without packet-to-packet interference.Ideally, a useful concurrency protocol should slow data transmissionrates as little as possible, although all transmissions may becompletely scheduled in advance or may occur according to an appropriateconflict resolution rule.

The prior art is replete with bus-oriented single-hop interconnection(SHI) techniques for improving channel concurrency within acommunication network. Such techniques are not limited to any particularphysical communication technology. Recent improvements in fiber optictransmission technology and the invention of the optical star couplerhave given rise to explosive growth of optical network applications.Optical data transmission technology is favored because of the very highdata transmission rates possible at optical frequencies. Unfortunately,optical bandwidth does little by itself to improve channel concurrencyin switched networks. Without circuit components capable of opticalswitching speeds, concurrency limitations will continue to be anobtrusive handicap for optical data transmission networks.

Not surprisingly, practitioners in the art have suggested improvednon-switched interconnection techniques for overcoming the limitationsof bus-oriented optical interconnection. Some proposals were intended toovercome inherent limitations of optical interconnection devices, suchas star couplers. For instance, in U.S. Pat. No. 4,543,666. Hans-HermannWitte, et al. disclose a method for interconnecting N subscribertransmitters to N subscriber receivers using a plurality of optical starcouplers. Witte, et al, use active optical repeaters to overcome theeffects of line attenuation. Their invention exploits the directionalityof star couplers to provide an echo-free bus-oriented interconnectionarchitecture that improves channel capacity by simplifying the necessarybus protocol. However, as with optical switching devices, the use ofactive optical repeaters increases the costs and reduces the reliabilityof their bus-oriented network. Recent publicized telephone systemfailures in the U.S. highlight the effects of these problems.

In U.S. Pat. No. 4,914,648, Anthony Acampora, et al, disclose a bus-likeMultiple Hop Interconnection (MHI) multichannel network that avoids theneed for agile optical switching devices. Their channels are allbus-like because any two transmitters are either connected to exactlythe same receivers or to disjoint sets of receivers. Acampora, et al,use a perfect shuffle network to simplify the necessary protocols underuniform traffic but they also pay the price of slower data transmissionbecause of the multiple hops (repeated active packet transmissions)required by their invention.

For a discussion of bus-oriented and non-bus-oriented SHI networks, seeMatthew T. Busche, et al, "On Optical Interconnection of Stations HavingMultiple Transmitters and Receivers," 1990 International Symposium onInformation Theory and its Applications (ISITA '90), Hawaii, U.S.A.,Nov. 27-30, 1990, session 63-3, pp. 967-970. See also, Y. Birk, et al,"Bus-Oriented Interconnection Topologies for Single-Hop Communicationsamong Multi-Transceiver Stations," IEEE Infocom'88, pp. 558-567, IEEEComputer Society Press, 1988. For an early discussion ofnon-bus-oriented networks, see Y. Birk, "Concurrent Communication AmongMulti-Transceiver Stations Over Shared Media", PhD Dissertation,Stanford University, Dec. 1986.

As used in the art and discussed by Birk, uniform traffic meanssubstantially equal data traffic across different "types" of sourcestation transmitters. Scheduled traffic implies a round-robintransmission schedule and not a random or "on-demand" schedule. Strictlyspeaking, this means that there is the same amount of traffic betweenany source/destination pair. However, so long as the correct "types" ofsource stations transmit in each time slot and the destination are asscheduled, the full channel concurrency will be attained. Thus, if onesource station of a given type has above average traffic for a givendestination and another source station of the same type has less trafficfor the same destination, the schedule can be modified to allocateadditional slots to the former at the expense of the latter. A similarargument applies if source stations have a single transmitter anddestination stations have multiple receivers. Moreover, even if thetraffic is not exactly uniform, the resulting degradation in concurrencyis gradual because only some of the time slots are underutilized. Tooperate an interconnection network with a given schedule, it isnecessary to synchronize the stations so they know when to begintransmitting. This can be done using a central "clock" whose signal isdistributed to all source station or by any other suitable means knownin the art.

Multichannel capacity is defined as the product of data rate andconcurrency, as is known in the art. Busche, et al, observe that msource stations having p transmitters per station can be interconnectedwith a destination stations having one or more receivers per stationusing either bus-oriented or non-bus-oriented SHI's. However, becausemaximum possible transmission rate is believed to be inverselyproportional to the power loss along the path, they suggest that theoptical power-split losses in passive non-bus-oriented SHI multichannelnetworks using multiple optical star couplers will limit the maximumpossible multichannel capacity to less than the capacity alreadyavailable in bus-oriented SHI networks.

Birk discusses non-bus-oriented SHI's that are organized so that eachtransmitter of a source station (SS) is directly connected to some setof destination stations (DS's), where the sets of DS's for differentSS's can be chosen independently of one another. This concept differsfrom bus-oriented SHI's, which require the sets of DS's connected to anytwo transmitters, one from each of two distinct SS's, to be eitheridentical or disjoint. Succinctly, a bus-oriented SHI is limited to aconcurrency of p (number of transmitters per SS) but has an optimalpower spreading loss factor of n/p.

For SS's having p=2 transmitters, a passive non-bus-oriented SHI of mSS's to n DS's with direct connections from each SS to every DS islimited in size to about n=20 or so because the power transmitted byeach SS is divided by n² /2 at every DS. This division occurs because ofthe two star coupler stages needed to make such a connection. A first (1by n/2) star coupler splits the signal transmitted from a single SStransmitter to n/2 branches and a second (n by 1) star coupler joins allSS outputs destined for a single DS input. As is known in the opticalart, the star coupler introduces an optical power loss equal to themaximum of the number of outputs or inputs. Thus, in this example, bothfirst and second coupler stages reduce optical signal power by n. Thetotal network power-split loss is then n*n/2 or n² /2 .

Increasing the number of optical transmitters to p at each SS willdecrease the number of receivers that must sense a single transmitter,thereby increasing the power available at the DS receiver and reducingthe effective power loss factor to n² /p. Adding active devices can alsoincrease available network connectivity, but only by increasing cost,complexity and reliability problems. Succinctly, such a non-bus-orientedSHI offers an improved concurrency of k=( log_(p) n choose (p-1)=(log_(p) n )!/(p-1)!/( log_(p) n -p+1)! but suffers with an optimal powerspreading loss factor of n² /p.

There is a strongly felt need in the optical network art for such ahigh-concurrency passive SHI technique for interconnecting numbers ofsource stations and destination stations well above the existingpractical limit of n=20. Increasing n is desired because it leads toincreased non-bus-oriented multichannel capacity resulting from improvedconcurrency k. Of course, the theoretical upper limit on passive networksize is governed the same linear power spreading loss factor n/p knownfor bus-oriented networks because each SS within a passive SHI networkmust be connected to every DS by a single-hop link. However, reducingthe power spreading factor from n² /p to n/p would vastly improvepassive network channel capacity at higher values of maximum concurrencyk. Thus, a need is felt for an interconnection wiring technique thatwill reduce power spreading losses in passive non-bus-oriented SHI'sfrom a factor of n² /p to a factor closer to the theoretically optimumvalue of n/p. The associated problems and unresolved deficiencies areclearly felt in the art and are solved by the present invention in themanner described below.

SUMMARY OF THE INVENTION

The present invention concerns a scheme for wiring the interconnectionbetween a set of source stations (SS's), each having p transmitteroutputs, and a set of destination stations (DS's) whereby the power lossand complexity are essentially proportional to n/p. It is a primaryadvantage of this invention that the parallelism or concurrency k=(log_(p) n choose (p-1)=( log_(p) n )!/(p-1)!/( log_(p) n -p+1)! can beattained without resorting to active optical devices or multiple-hopinterconnection (MHI) schemes or reducing data rate. This invention alsominimizes the number of fibers and couplers required for implementingthe interconnection.

An advantage of this invention is that the disclosed interconnectionschemes can be applied to other technologies including microwavewaveguides, electrical conductors and the like, as well as opticalconductors.

An important feature of the invention is that the number of componentsand number of interconnections is optimized as well as the powerspreading loss.

An object of the invention is to connect a set of m SS's, each with atleast p=2 transmitters, to a set of n DS's, each with a single receiver,such that the power and complexity are essentially proportional to n/p.

It is another object of this invention to make such an interconnectionwithout requiring active optical repeaters or amplifiers.

It is another object of this invention to make such an interconnectionwithout requiring active optical repeaters or amplifiers.

It is yet another object of this invention to effect such aninterconnection so that all SS's are connected to every DS by a singleseries of passive links, referred to as a "single hop".

It is yet another object of this invention to minimize the numbers ofcomponents and connections necessary to achieve such an efficientsingle-hop multichannel system.

In the described invention, the coupler stages necessary to directlyconnect SS output to DS inputs are combined in a manner that forces eachcoupler in the multichannel to have equal or nearly equal numbers ofinputs and outputs. It is a particular advantage of such a combinationthat the power spreading loss through any single coupler is notsubstantially more than a factor equal to the number of coupler outputs.

Another feature of this invention exploits the connection symmetriesamong the DS's. In this scheme, the path from a SS transmitter isconnected to a DS receiver through several coupler stages. These stagesare necessary because of the non-bus-oriented nature of the symmetries,wherein no two receivers hear exactly the same set of transmitters. Forthe important case of p=2, the specifications for each of the threenecessary coupler stages are determined by the following two rules:

(a) the product of the number of outputs of the first stage, the numberof outputs of the second stage and the number of outputs of the thirdstage must be equal to the number of DS's divided by the number oftransmitters (p) within each SS; and

(b) the number of inputs and outputs for each coupler within any stagemust differ by no more than one.

These rules result in an interconnection power spreading loss thatapproaches (for p=2) the theoretical minimum of n, which is the numberof DS's. The method of this invention can be extended to cases where p>2by exploiting symmetry, separating transmitters by "type", and mergingand splitting the connections to obtain "square" couplers.

In networks where k=log₂ n=integer, the power spreading loss will beprecisely equal to (n). For networks where k is odd, where the number ofSS's is not an even multiple of k, or where the number of SS's is not aneven multiple of k, or where the number of DS's is not an exact multipleof 2^(k), this invention will result in an optimal power spreading losssomewhat greater than the theoretical minimum of (n).

This invention can be readily extended to odd values of k by augmentingeither the DS's or SS's with dummy stations until n=2^(k) with k even.The invention can be extended to the case where, for p=2, an evenconcurrency of (log₂ n)+1 can be achieved by renumbering all DS's with alist of all binary numbers between zero and (2n-1) having exclusivelyodd parity (or exclusively even parity).

An alternative embodiment for reducing power loss in a passive opticalinterconnection exploits the symmetry among SS's partitioned by "type"into groups having no more than k members. Because any two SS's havingthe same number (i modulo k) are identically connected to the n DS's, asingle stage of (n/k) by (n/2) star couplers followed by a final stageof k by 1 couplers can be used to make the connections. An importantadvantage of this alternative embodiment is that the power-split loss isreduced from n² /2 to n*log₂ n/2, a substantial improvement over thestraightforward interconnection technique known in the art.

Advantageously, interconnections made according to the invention can beused to carry analog as well as digital information. Another benefit isthat a signal follows a unique path from each SS to each DS, therebyavoiding any possibility of self-interference arising from multipathtransmissions. Another feature of this invention is that mutualinterference can be avoided by scheduling no more than k concurrenttransmissions chosen to prevent the simultaneous arrival of more thanone signal at any DS in a manner obvious to practitioners in the opticalnetwork arts. One schedule that achieves the claimed concurrency isdescribed by Birk, et al in their 1990 reference cited and incorporatedbelow.

The described invention has application to non-bus-oriented networksbecause the sets of DS's attached to transmitters of different SS's inthe network need not be disjoint identical sets. However, theseteachings may also be applied to bus-oriented single-hop interconnectionarchitectures.

The foregoing, together with other features and advantages of myinvention, will become more apparent with reference to the followingspecifications, claims, and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the invention, reference is nowmade to the following detailed description of the embodimentsillustrated in the accompanying drawings, wherein:

FIG. 1 illustrates a single-hop interconnect network for the scheduledconcurrent transmission k=2 messages;

FIG. 2 illustrates a two-stage embodiment of the invention n=4 and k=2;

FIG. 3 illustrates a two-stage embodiment of the invention for n=8 andk+1=4;

FIG. 4 illustrates a three-stage embodiment of the invention for n=8 andk+1=4; and

FIG. 5 illustrates a three-stage embodiment of the invention n=64 andk=6.

DISCUSSION OF THE PREFERRED EMBODIMENTS

FIG. 1 illustrates a prior art scheme for interconnecting sourcestations and destination stations with a non-bus-oriented structure. Theprior art scheme does not, however, optimize power spreading loss. Thisscheme is discussed in detail by Y. Birk, et al, "On the Uniform-TrafficCapacity of Single-Hop Interconnections Employing Shared DirectionalMultichannels", IBM Research Report RJ7859 (72519), Dec. 5, 1990. Thisdocument is included herein in its entirely by the reference.

In FIG. 1, a shared directional multichannel 8 connects a set of nsource stations (SS's), one of which is indicated by 10, each with p=2transmitter outputs (reference numeral 11 on SS10), to a set ofdestination stations (DS's), one of which is indicated by 12, each witha single receiver input (reference numeral 13 on DS12). These two setscan also be the two halves of the same set of stations. For each (SS,DS) pair, the channel specifies which of the two SS transmitters can beheard by the DS receiver. Each SS is connected to all of the DS's by anarrangement of couplers and point-to-point transmission links. Forexample, each transmitter output 11 of the SS 10 is connected to aninput port of a transmissive (1 by 2) coupler 15. Each of the two outputports of the coupler 15 is connected to a respective point-to-pointtransmission link 17. At the receiver input 13, a four-to-onetransmissive star coupler 19 has each of its input ports connected to apoint-to-point link from a respective one of the four couplers 15. Theentire interconnection including output couplers, point-to-point passivelinks, and input couplers is referred to as a "multichannel".

With the connections chosen in the manner shown in FIG. 1 andtransmission scheduled appropriately (e.g., as taught by Birk, et al intheir 1990 reference cited and incorporated above), the illustratedmultichannel can sustain k=log₂ n concurrent, non-interferingtransmissions for a uniform traffic pattern.

The passive shared directional multichannel example shown in FIG. 1 isfor n=4 DS's with the interconnections chosen to permit k=2 concurrenttransmissions from two SS groups of two SS's each. Note that each SS issequentially numbered from i=1 to k within each SS group. For each SS,p=2 individual transmitter outputs are numbered from l=1 to 2. Each DShas one receiver input and is numbered from j=1 to n. For the purposesof determining the individual connections, each DS is identified by anumber (j radix 2) or binary j in the illustrated case. Each SS isconnected directly to every DS through at least one transmitter output.There are no routing switches and no intermediate stations. The i^(th)SS use the first (l=1) transmitter output 11 to connect to the j^(th) DSonly if the i^(th) digit in the binary representation of the number j iszero (l-1=0); otherwise, the i^(th) SS uses the second (l= 2)transmitter for the connection (l-1=1).

In the multichannel scheme of FIG. 1, when a SS transmits using one ofits transmitters, that transmission is heard by all DS's whose receiversare connected to that transmitter. A DS receives a message successfullyif and only if that message is addressed to the DS and the DS cannothear any other transmissions at the same time. When a DS hears twomessages simultaneously, there is a "collision" and neither message isheard. By appropriately scheduling the transmissions, it is possible totransmit k messages concurrently (one from each SS type) withoutcollision. When there are equal amounts of traffic between each SS andDS, this interconnection has a capacity of k conventional channels, yeteach SS uses only two transmitters and each DS uses only one receiver.This interconnection is symmetric in the sense that the roles of SS andDS can be reversed with no change in capacity.

When there are more than k SS's, those with identical numbers (i modulok) all have identical connections to the DS's with the scheme and areconsidered to be of the same "type". When the number of SS's equals thenumber of DS's, the two sets of stations can either be viewed asseparate or simply as the two halves of the same n stations. Eachtransmitter is then connected to n/2 receivers and each receiver isconnected to n transmitters as illustrated in FIG. 1.

The passive directional non-bus-oriented SHI network scheme describedabove for FIG. 1 lends itself to an implementation using optical fibersand directional star couplers. A directional star coupler is an elementwith several input fibers and several output fibers and is well-known inthe art. An optical signal presented at any input is spread among alloutputs but does not reemerge from any of the input fibers.

When all fibers used in a star coupler are of equal cross-sections, asis usually the case, the ratio of power presented at an input to thatcoming out of any output line is the maximum of the number of inputs orthe number of outputs. Therefore, for the network shown in FIG. 1, anoptical signal must travel through a (1 by n/2) coupler followed by a (nby 1) coupler and the power at the receiver is the transmitted powerdivided by n² /2. This quadratic power-loss factor severely limits thenumber of stations that can be passively interconnected using thestraightforward scheme illustrated in FIG. 1. Because direct(noncoherent) detection is normally used in optical networks,insufficient optical signal power requires that active devices be addedto amplify the optical signals.

Any wiring of the interconnection shown in FIG. 1 must permit the signalfrom each transmitter output 11 to be split n/2 ways because it mustreach n/2-receiver inputs 12 if every SS is to reach all n DS's and eachSS has only two transmitter outputs 11. Similarly, n signals must becombined at each receiver input 13 because each DS is connected to nSS's in the example shown. Therefore the minimal theoretically possiblepower split factor is n/2.

In their December 1990 reference incorporated above, Birk et al teach ageneral connection rule for vales of p≧2 without considering powerspreading losses or wiring layout. The n=p^(k) DS's (not shown) arenumbered with vales of (j radix p) each having k digits. The values of jrange from zero to (p^(k) -1). The number of SS "types" is set to k=(log_(p) n choose (p-1)=( log_(p) n /(p-1)!/( log_(p) n -p+1) ! and eachSS is represented by a k-digit binary number (i radix 2) having "1" inexactly (p-1) places and "0" in the (k-p+1) remaining places. Of course,for p=2, k=(log₂ n choose (2-1)=log₂ n.

The rule for selecting the 1^(th) transmitter in the i¹ SS to beconnected to the j^(th) DS requires that the (p-1) digits of (j radix p)bu summed in the positions in which (i radix 2) has ones (summation ofthe digit by digit product of i*j). The resulting sum, modulo p, is thevalue of 1 required for the connection, where 1 ranges from zero to(p-1). This method and its extension to multichannels for multiplereceivers as well as optimal transmission scheduling techniques will bebest appreciated by referring to the 1990 Birk, et al referenceincorporated above.

THE INVENTION

The invention provides a wiring scheme for the non-bus-oriented SHInetwork shown in FIG. 1 that attenuates the signal by only a factor ofn/p and is optimal. The schemed of the invention also minimizes thenumber of fibers and couplers required for implementing theinterconnection. The wiring scheme illustrated in FIG. 1 that makesdirect connections from the outputs of couplers 15 to the inputs ofcouplers 19 separates the splitting and combining stages, therebyincurring the power budget penalty twice. In the splitting phase, thenumber of outputs of a first stage coupler 15 determines the power splitratio. In the combining phase, the number of inputs to a second stagecoupler 19 determines the split ratio. The key element of this inventionis the combination of the functions of these two stages so that eachcoupler in the connection path has equal or nearly equal numbers ofinputs and outputs. Such a coupler is referred to hereinafter as a"substantially square" coupler. Preferably, the input port count of asubstantially square coupler should differ from the output count by nomore than one to minimize the power spreading loss in the multichannel.

FIG. 2 shows a first interconnection scheme according to the inventionfor m=4 SS's and n=4 DS's using only two coupling stages. Thenomenclature for FIG. 2 is similar to that discussed above in connectionwith FIG. 1. The network connection rule is that the 1^(th) transmitteroutput 21 of the i^(th) SS within each SS group must be connected toreceiver input 23 of the j^(th) DS such that the i^(th) digit of theinteger (j radix 2) is equal to (l-1). The i^(th) digit of binaryinteger j is determined by numbering from the least significant digit inthe example shown in FIG. 2. When the numbering scheme is started at j=0as shown, the i^(th) digit may be determined in any consistent manner.

Because any two SS's with the same number (i modulo k) have identicalconnections, each set of individual transmitter outputs 21 (there are 2ksuch sets each with n/k such transmitter outputs) is first connected tothe inputs of an (n/k) by (n/2) star coupler 18. The star coupler 18replicates each transmitter output 21 (n/2) times and combines sets of(n/k) outputs 21 that are to reach the same receiver inputs 23. For anygiven receiver input 23, one output of each coupler 18 is connected to ak by 1 coupler 20. The output of coupler 20 is connected to receiverinput 23. Examination of FIG. 2 will verify that the total power splitfactor of this scheme is nk/2=n(log₂ n)/2, an expression that is alwaysless than n² /2. Thus, the scheme shown in FIG. 2 represents asubstantial improvement in power-spreading loss over the straightforwardscheme illustrated in FIG. 1.

For interconnection where n/k is not an integer, dummy SS's can be addeduntil the total number is an integer multiple of k. That is, the SSgroup size is n/k , which is defined as the smallest integer greaterthan (n/k).

For odd values of k, when p=2, the scheme shown in FIG. 2 can beextended to permit k+1 concurrent transmissions in the mannerillustrated in FIG. 2. For this discussion, k is defined as before butconcurrency is extended by one channel to k+1. FIG. 3 shows m=n=8 SS'sdivided into (n/k+1) SS groups, each SS within a group numbered from i=1to (k+1), and n=8 DS's, which are numbered according to a special ruleof this invention. If k were even, the concurrency would be limited tok= log₂ n . Because k is odd, the concurrency can be increased to k+1 bynumbering all the DS's with a binary number j selected from the group ofnumbers between 0 and 2^(k+1) -1 according to the parity. As shown inFIG. 3, each of 2^(k+1) -1 DS's is numbered with (j radix 2) having anodd parity. Of the 16 possible values for j, 8 odd parity and 8 haveeven parity. The 8 odd-parity values for j are used to number the 8 DS'sin the manner shown in FIG. 3. Eight even-parity values are alsoavailable and can alternatively be used, as disclosed by Busche et al,cited above.

The remainder of the two coupling stage scheme for interconnecting nDS's and m SS's for odd values of k is identical to that discussed abovein connection with FIG. 2. The first-stage star coupler is selected as a(n/(k+1) by (n/2) coupler 22. All individual transmitter outputs 31 ofthe same type (with identical connections) are then connected to theinputs of a coupler 22. The second stage coupler is defined as a (k+1)by 1 coupler 24 and the output of coupler 24 is connected to receiverinput 33 in the manner shown. Finally, the outputs of couplers 22 areconnected to the inputs of coupler 24 in a manner such that the l^(th)transmitter output 31 of the i^(th) SS within each SS group is connectedto the receiver input 33 of the j^(th) DS such that the i^(th) digit ofbinary integer j is equal to (l-1). Because of the selection of valuesfor j having odd parity from a group numbering 2^(k+1) -1, each value ofj has 4 bits, thereby permitting four sets of DS's to be systematicallyselected for k+1=4 concurrency.

Note that the power spreading factor for the scheme shown in FIG. 3 is16. This compares favorably with the power spreading factor for FIG. 1of n² =64 but does not match the power spreading factor for FIG. 2 ofnk/2=12. Thus, concurrency has increased to (k+1) in a manner thatreduces the number of couplers required but does nothing to improve thepower spreading factor that results form merely adding dummy SS's andDS's to force n=16 and proceeding to connect according to the rulediscussed above for FIG. 2.

The next element of the invention is the addition of a third stage ofcouplers (stage-2) between the two stages used in the scheme discussedabove in connection with FIG. 2, which takes advantage of connectionsymmetries on the DS side of the network. Recalling that the l^(th)transmitter output 21 used by the i^(th) SS to reach DS number j isdetermined by value of the i^(th) bit in the binary representation of j,it follows that all DS's with binary numbers having the first (mostsignificant) (k/2) bits in common also have identical connections toSS's of the first (k/2) types. Similarly, all DS's with numbers j havingthe last (k/2) bits in common also have identical connections to theSS's of the remaining (k/2) types. The number of such DS's in each caseis 2^(k/2). The following discussion uses general values for n and k butmay be best understood by referring to FIG. 5, which shows a three-stagecoupler network for k=6 and n=64.

To take advantage of the symmetry, 2*2^(k/2) stage-2 couplers 34 areused. One-half of the stage-2 couplers 34 are used to provide allpossible combinations of signals from the first (k/2) SS's (onetransmitter output 51 from each SS in each combination), and the othersare used to do the same for the remaining (k/2) SS's. Because eachcombination must reach some set of 2^(k/2) outputs.

A stage-2 coupler must have k/2 inputs because it combines this numberof signals. Note that the total number of outputs for all stage-2couplers is 2n. Each receiver input 53 must now be connected to theoutputs of the two stage-2 couplers 34 that carry the combined signalsof transmitter outputs 51 to which the respective DS must be connected.These two couplers 34 provide an output for the first half of the SS'sand an output for the appropriate combination of the second half of theSS's. Thus, the third stage of couplers 36 are simply n couplers of sizetwo by one.

Because p=2, any given transmitter output 51 is used in only one-half ofthe combinations involving its SS. Thus, the stage-one couplers 32 musthave one input and (2^(k/2-1)) outputs. FIG. 5 illustrates the optimalwiring scheme for k=6. Couplers are represented by circles or ellipsesand stations represented by rectangles or squares.

The next element of the invention is a technique for breaking the mergerof n/k signals into two steps. In the first step, groups of x signalsfrom transmitter outputs 51 having identical connections are combinedusing x by y couplers. The integers x and y have values yet to bedetermined. In the second step, one output from each coupler isidentified and those outputs are connected to the inputs of a newcoupler, which completes the merger.

The next element of the invention is to let the x by y couplers serve asthe stage-1 couplers 32 and let the stage-2 couplers 34 play both therole of completing the merger of n/k signals and their previous role ofcombination k/2 "types" of signals. Signals are of the same "type" ifthey come from the same l^(th) transmitter of SS's having the same valueof (i modulo k). The input count of a stage-2 coupler is therefore kz/2for some integer z.

The final element of the invention is to select the best values of x, yand z. Because the number of receivers reached by each transmitteroutput 51 is n/2 (where p=2) and the stage-3 couplers 36 can only haveone output, it follows that the product of the output count of a stage-1coupler 32 and the output count of a stage-2 coupler 34 must be at leastequal to n/2. To minimize the power split, this product is forced to beexactly equal to n/2 and the input count for any coupler is kept asclose as possible to the output count for that coupler; that is, allcouplers are forced to be "substantially square". These two conditionswill minimize the power split in the 3-stage interconnection embodiment.

In the following steps, a method is disclosed for computing the actualcoupler sizes and numbers required for a network of n DS's and m SS'swhere m≧k and where each DS has p=2 transmitter outputs. Although n, mand k are general, the following may be best understood by referring toFIG. 5.

(a) Stage-3 couplers 36 are (2 by 1) and n in number.

(b) Each transmitter output 51 must reach 2^(k/2-1) stage-2 couplers 34,which is the number of k/2-bit numbers in which one bit is fixed.Therefore, the output count for each stage-1 coupler 34 is y=2^(k/2-1).

(c) The number of clusters of transmitter outputs 51 having identicalconnections that have not yet been combined is equal to z. This issimply z=(m/k)/x.

(d) An (x, z) combination is chosen that minimizes the power split forthe 3-stage network. The first step in choosing (x, z) is to equate xand y, thereby making stage-1 coupler 32 exactly square. This forces z=m/(kx)=2^(k/2+1) /k. Thus, the number of inputs of stage-2 coupler 34 is(k/2)*z=2^(k/2) =√n. Conveniently, this is exactly the number of outputsof stage-2 coupler 34, thereby forcing all stage-2 couplers 34 to besubstantially square.

The above expressions for the directional coupler input and outputcounts may not produce integer results. To obtain proper integerresults, for even values of k:

(a) first compute a value for z and, if it is not an integer, performthe following two steps for both integer values of z adjacent thecomputed value;

(b) next compute a value for x= 2^(k) /kz (closest greater integer) andadd enough dummy SS's so that the total number of SS's is an integralproduct of kx. These dummy stations are added at the end of the actualSS's and neither they nor their connections actually exist; and

(c) finally compute y=2^(k/2-1) and compute the power-split factor equalmax (x,y}*max{kz/2,2^(k/2) }*2. If there were two possible values of z,choose the value of z that results in the smallest power-split factor.

The above steps can be generalized for other values of p by similarlyexploiting symmetries among the SS's and DS's to optimize the p>2connection rule discussed above. For even values of k, the inventionworks naturally with k "types" of SS's; that is, for SS partitions whereall SS groups have exactly k members except for a single group that mayneed to be filled with dummy SS's. For odd values of k, the inventionworks most simply with k+1 types of SS's. If desired, however, k typesmay be used for odd k and k+1 types for even k.

For values of p>2, additional coupling stages may be useful inoptimizing the power-split loss to a value approaching n/p. Inaccordance with the invention, the first two or more coupling stages(all but the final stage) must be configured to meet the two importantrequirements: (a) product of coupling stage output counts equaling (n/p)and (b) all couplers being substantially square. The wiring requirementsand coupler design procedure can be inferred without undueexperimentation by extension of the methods discussed above inconnection with the p=2 examples illustrated in FIGS. 4 and 5.

For odd values of log₂ n=k , when p=2, the interconnection can be wiredto obtain log₂ n+1 concurrent transmissions in accordance with thisinvention in the following manner. First, each DS member is renumberedwith a set of numbers j selected from zero to (2n-1) as discussed abovein connection with FIG. 3. Each DS thus corresponds to a (k+1) bitnumber j, although only half the possible combinations are used. Thebits in the remaining numbers are symmetric so that any combination ofbit values occurs exactly half the number of times it would haveoccurred if all 2^(k+1) numbers were used. Couplers are then selected inaccordance with the above-described schemes. Note that the number ofoutputs of the stage-2 coupler is now 2.sup.(k-1)/2. Also, clusters ofSS's with identical connections now contain n/(k+1) SS's and there arenow k+1 "types" of SS's.

Thus, for the special case where p=2 and concurrency equals k+1, thestage-1 and stage-2 couplers are identical square couplers having2.sup.(k-1)/2 inputs and outputs and the stage-3 couplers are all 2 by 1directional couplers.

FIG. 4 shows the same SS and DS configuration illustrated in FIG. 3, forn=8 and k+1=4. The same scheme for attaining concurrency of (k+1) forodd values of k is employed in connection with the scheme shown in FIG.3. As before, values of j having only even parity could just as well beused. In FIG. 4, coupler stage 1 includes n=8 couplers 26, coupler stage2 includes n=8 couplers 28 and coupler stage 3 includes n=8 couplers 30.The input and output counts for directional couplers 26, 28 and 30 aredetermined by the method described above for minimizing power-split losswith three coupler stages.

Referring to FIG. 4, note that stage-1 couplers 26 are (2×2) as arestage-2 couplers 28. Stage-3 couplers 30 are (2×1) and all connectionsbetween couplers 26, 28 and 30 are such that the l^(th) transmitteroutput 41 of the i^(th) SS within each SS group is connected to thereceiver input 43 of the j^(th) DS such that the i^(th) digit of the oddparity integer j is equal to (l-1). Comparing the 3-stage implementationfor n=8 and k+1=4 in FIG. 4 with the 2-stage multichannel of FIG. 3 forthe same stations shows that the addition of a third stage has reducedthe power-split factor from 16 to 8, thereby doubling the availablepower at each receiver input 43. The necessary transmission schedule forj having odd parity is a trivial extension of the even-parity scheduleknown in the art is disclosed in the Busche, et al reference citedabove.

To understand the general case for even-valued k, consider the examplein FIG. 5. A 3-stage interconnection is illustrated for concurrency k=6between m=64 SS's and n=64 DS's. To compute the numbers specifying thestage-1 couplers 32, the stage-2 couplers 34 and the stage-3 couplers36, note that there are 64 stage-3 couplers, one per DS, each of size 2by 1. Note that there are 2*2^(k/2) =16 stage-2 couplers 34. The firsteight couplers 34 represent all combinations of transmitter output 51choices from the first k/2=3 "types" of SS's and the remaining eightrepresents the choice from the remaining three types of SS's. The numberof outputs for stage-2 coupler 34 is 2^(k) /2=8.

Because kz/2=3z=8, the trial values for z are two and three, andy=2^(k/2-1) =4.

Considering a first value for z=2, x= n/kz =6. The resulting power splitis 6*8*2=96.

For z=3, x= n/kz =4. The resulting power split is 4*9*2=72. Thus, z=3and x=4 are selected because that provides the minimum power split of72. Note that in this example, it is not possible to force thepower-split factor down to the ideal value of n=64 because of theasymmetry resulting from k=6 not being an exact power of p=2.

With x=4, the number of SS's is augmented with dummies to reach thesmallest number that is an integer multiple of kx and also greater thanor equal to n. This number is 72, which is reached by adding two dummySS's to fill the third SS group 38 in cluster III and 6 dummy SS's toform a fourth SS group 40 within cluster III as best seen in FIG. 5. Theinterconnection is now constructed as follows.

(a) Partition the SS's in twelve SS groups of k=6, each containing oneSS of each "type".

(b) Partition the SS groups into z=3 clusters of four groups each.

(c) In each cluster there are not four SS's in each "type" withidentical connections (one SS in each of four SS groups). Select eachset of four transmitter outputs 51 having identical connections andconnect them to the four inputs of 4×4 coupler 32. The outputs of thestage-1 couplers 32 can now be viewed as three sets of SS's, each ofwhich has one SS of each of the four types, and each transmitter of eachsuch SS having four output lines carrying identical signals.

(d) Next connect outputs of the stage-1 couplers 32 to inputs of thestage-2 coupler 34 following the example of stage-2 coupler H110 seen inFIG. 5. Connect to H110 the second coupler 42 of the first pair in eachset, the second coupler 44 of the second pair in each set and the firstcoupler 46 of the third pair in each set as best seen in FIG. 5.

(e) Finally connect one input of a stage-3 coupler 36 to the output ofthe stage-2 coupler Hxxx, where xxx is the value of the first (mostsignificant) three bits in the binary DS number j, and connect the otherinput to the output of the stage-2 coupler Lyyy where yyy is the valueof the last (leaf significant) three bits in the binary DS number j.

While the above discussion considers an exact method for construction ofthe multichannel wiring using either a 2-stage or a 3-stageinterconnection for the most interesting case where p=2, the methods ofthis invention can easily be applied to other related networks. Forinstance, this invention can be used to optimize interconnectionnetworks using couplers with more inputs and/or outputs than required(e.g. such as are available off the shelf). Also this invention can beapplied to implementations that do not take full advantages of thescheme and use only a part of the elements or use them suboptionally.For example, a scheme that uses more inputs than necessary in thestage-3 couplers can be suboptimized using this invention. Also, thecouplers defined by this invention can be implemented using acombination of a plurality of smaller optical star couplers in a mannerwell known in the art.

Obviously, other embodiments and modifications of this invention willoccur readily to those of ordinary skill in the art in view of theseteachings. Therefore, this invention is limited only by the followingclaims, which include all such obvious embodiments and modifications.

I claim:
 1. A shared directional multichannel system for scheduleduniform traffic of up to k concurrent transmissions from m sourcestations to n destination stations, each said destination stationincluding one receiver input, each said source station including ptransmitter outputs and all said source stations being partitioned intoat least one source station group such that no more than one said sourcestation group contains less than k source stations, wherein k, m, n andp are positive non-zero integers and m≧k=( log_(p) n choose (p-1), thesystem comprising:a first stage including at least (p*k) firstdirectional couplers, each said first directional coupler having n/poutputs and no more m/k inputs, all said inputs of each said firstdirectional coupler being connected to transmitter outputs from arespective source station group; a second stage including n seconddirectional couplers, each said second directional coupler having atleast k inputs and one output, said output being connected to adestination station receiver input; and interconnection means forcoupling said first stage to said second stage by connecting said firstdirectional coupler outputs to said second directional coupler inputs ina manner such that the l^(th) transmitter output of the i^(th) sourcestation within each said source station group is connected to thereceiver input of the j^(th) destination station, where the modulo p sumof the digits of (j modulo p) in positions corresponding to unit digitpositions in (i radix 2) is equal to (l-1).
 2. The shared directionalmultichannel system of claim 1, wherein:p=2 and each said source stationincludes two transmitter outputs.
 3. The shared directional multichannelsystem of claim 2 for scheduled uniform traffic of up to (k+1)concurrent transmissions from said source stations, wherein:said sourcestations being partitioned into at least one source station group suchthat no more than one said source station group contains less than (k+1)source stations; and said interconnection means further includes meansfor connecting the l^(th) transmitter output of the (k+1)^(th) sourcestation within each said source station group to the receiver input ofthe j^(th) destination station, where the parity of binary integer j isequal to (l-1).
 4. The shared directional multichannel system of claim3, wherein:said first directional coupler includes at least one opticalstar coupler; said second directional coupler includes at least oneoptical star coupler; and said interconnection means includes means forconducting optical signals.
 5. The shared directional multichannelsystem of claim 4 wherein:said optical star coupler stages comprise aplurality of smaller optical star couplers interconnected to form asingle larger said coupler.
 6. The shared directional multichannelsystem of claim 1, wherein:said first directional coupler includes atleast one optical star coupler; said second directional coupler includesat least one optical star coupler; and said interconnection meansincludes means for conducting optical signals.
 7. The shared directionalmultichannel system of claim 6 wherein:said optical star coupler stagescomprise a plurality of smaller optical star couplers interconnected toform a single larger said coupler.
 8. The shared directionalmultichannel system of claim 1 wherein:one or more source stationswithin at least one said source station group and the respectiveconnections are absent.
 9. A shared directional multichannel system forscheduled uniform traffic of up to k concurrent transmissions from msource stations to n destination stations, each said destination stationhaving one receiver input, each said source station having twotransmitter outputs and all said source stations being partitioned intoat least one source station group such that no more than one said sourcestation group contains less than k source stations and all said sourcestation groups being partitioned into z clusters of no more than m/kzgroups, wherein k, m, n, and z are positive nonzero integers, m≧k= log₂n and z=m/kx is selected to minimize the value of {max(x,y)*max(m/(2x),n/(2y))} where y=√n/2, said system comprising:a first stage including2kz first directional couplers, each said first directional couplerhaving √n/2 outputs and no more than m/kz inputs, all said inputs ofeach said first directional coupler being connected to transmitteroutputs from a respective source station group; a second stage including2√n second directional couplers, each said second directional couplerhaving at least kz/2 inputs and √n outputs; first interconnection meansbetween said first stage and said second stage for connecting said firstdirectional coupler outputs to said second directional coupler inputssuch that the l^(th) transmitter output of the i^(th) source stationwithin each said source station group is connected to the receiver inputof the j^(th) destination station, where the i^(th) digit of binaryinteger j is equal to (l-1); a third stage of n third directionalcouplers, each said third directional coupler having two inputs and oneoutput, said output being connected to a destination station receiverinput; and second interconnection means between said second stage andsaid third stage for connecting said second directional coupler outputsto said third directional coupler inputs such that the l^(th)transmitter output of the i^(th) source station within each said sourcestation group is connected to the receiver input of the j^(th)destination station, where the i^(th) digit of binary integer j is equalto (l-1).
 10. The shared directional multichannel system of claim 9 forscheduled uniform traffic of up to (k+1) said concurrent transmissionsfrom said source stations, wherein:said source stations are partitionedinto at least one station group such that no more than one said sourcestation group contains less than (k+1) source stations; and said firstand second interconnection means each further includes means forconnecting the l^(th) transmitter output of the (k+1)^(th) sourcestation within each said source station group to the receiver input ofthe j^(th) destination station, where the parity of binary integer j isequal to (l-1).
 11. The shared directional multi-channel system of claim10 wherein:said first directional coupler includes at least one opticalstar coupler; said second directional coupler includes at least oneoptical star coupler; said third directional coupler includes at leastone optical star coupler; and said first and second interconnectionmeans include means for conducting optical signals.
 12. The shareddirectional multichannel system of claim 11 wherein:said optical starcoupler stages comprise a plurality of smaller optical star couplersinterconnected to form a single larger said coupler.
 13. A shareddirectional multichannel system according to claim 9 wherein:said firstdirectional coupler includes at least one optical star coupler; saidsecond directional coupler includes at least one optical star coupler;said third directional coupler includes at least one optical starcoupler; and said first and second interconnection means include meansfor conducting optical signals.
 14. The shared directional multichannelsystem of claim 13 wherein:said optical star couplers comprise aplurality of smaller optical star couplers interconnected to form asingle larger said coupler.
 15. The shared directional multichannelsystem of claim 9 wherein:one or more source stations within at leastone said source station group and the respective connections are absent.16. A method for interconnecting a first set of m source stations of ktypes, each said source station having p transmitter outputs, to asecond set of n destination stations, each said destination stationhaving one receiver input, such that each source station is uniquelyconnected to every destination station by a single-hop directionalconnection whereby collision can be avoided by scheduling no more than kconcurrent transmissions from said m source stations, wherein k, m, nand p are positive nonzero integers and m≧k=( log_(p) n choose (p-1)),the method comprising the steps of:partitioning said m source stationsinto at least one source station group such that no more than one saidsource station group contains less than k source stations; andconnecting the l^(th) transmitter output of the i^(th) source stationwithin each said source station group to the receiver input of thej^(th) destination station, where the modulo p sum of the digits of (jmodulo p) corresponding to unit digit positions in (i radix 2) is equalto (l-1), each said connection includinga first link between said l^(th)transmitter output and an input of the first in a series of at least twocoupling stages, each said coupling stage having a plurality ofsubstantially square directional couplers, each said substantiallysquare directional coupler including a first plurality of coupler inputsand a second plurality of coupler outputs where said first and secondpluralities are substantially equal, with the outputs of each saidcoupling stage connected to the inputs of the immediately subsequentcoupling stage, a penultimate link between an output of the last in saidseries of at least two coupling stages and an input of a final couplingstage of at least n number of final directional couplers, each saidfinal directional coupler having p inputs and a single output, and afinal link between the j^(th) output of said final coupling stage andthe receiver input of said j^(th) destination station.
 17. The method ofclaim 16, wherein:p=2 and each said source station includes twotransmitter outputs.
 18. The method of claim 17 for uniform traffic ofup to (k+1) concurrent transmissions, wherein:in said partitioning stepno more than one said source station group contains less than (k+1)source stations; and said connecting step includes the step ofconnecting the l^(th) transmitter output of the (k+1)^(th) sourcestation within each said source station group to the receiver input ofthe j^(th) destination station, where the parity of binary integer j isequal to (l-1).
 19. The method of claim 18 wherein m=n, furtherincluding the step of co-locating every said source station within saidfirst set with one respective said destination station within saidsecond set.
 20. The method of claim 16, further comprising, followingsaid partitioning step, the step of:selecting said first and secondpluralities of inputs and outputs for said series at least two couplingstages of substantially square directional couplers so that thearithmetic product of the at least two said second pluralities ofcoupler outputs is substantially equal to (n/p).
 21. The method of claim16, wherein m=n, further including the step of co-locating every sourcestation within said first set with one respective said destinationstation within said second set.
 22. The method of claim 16, wherein saidconcurrent transmission, said transmitter outputs, and said receiverinputs include optical signals.
 23. A method for interconnecting a firstset of m source stations of k types, each said source station having ptransmitter outputs, to a second set of n destination stations, eachsaid destination station having one receiver input, such that eachsource station is uniquely connected to every destination station by asingle-hop directional connection whereby collision can be avoided byscheduling no more than k concurrent transmission from said m sourcestations, wherein k, m, n and p are positive nonzero integers m≧k=(log_(p) n choose (p-1)), the method comprising the steps of:partitioningm source stations into at least one source station group such that nomore than one said source station group contains less than k sourcestations; and connecting the l^(th) transmitter output of the i^(th)source station within each said source station group to the receiverinput of the j^(th) destination station, where the modulo p sum of thedigits of (j modulo p) in positions corresponding to unit digitpositions in (i radix 2) is equal to (l-1), each said connectionincludinga first link between said l^(th) transmitter output of thei^(th) source station and an input of a first coupling stage of at least(p*k) number of directional couplers each having n/p outputs and no morethan n/k inputs, a second link between an output of said first couplingstage and an input of a second coupling stage of at least n number ofdirectional couplers having no less than k inputs and one output, and athird link between an output of said second coupling stage and thereceiver input of said j^(th) destination station.
 24. The method ofclaim 23, wherein:p=1 and each said source station includes twotransmitter outputs.
 25. The method of claim 24 for uniform traffic ofup to (k+1) concurrent transmission, wherein:in said partitioning stepno more than one said source station group contains less than (k+1)source stations; and said connecting step includes the step ofconnecting the l^(th) transmitter output of the (k+1)^(th) sourcestation within each said source station group to the receiver input ofthe j^(th) destination station, where the parity of binary integer j isequal to (l-1).
 26. The method of claim 25 wherein m=n, furtherincluding the step of co-locating every source station within said firstset with one respective said destination station within said second set.27. The method of claim 23 wherein m=n, further including the step ofco-locating every source station within said first set with onerespective said destination station within said second set.
 28. Themethod of claim 23 wherein said concurrent transmissions, saidtransmitter outputs, and said receiver inputs include optical signals..Iadd.
 29. A shared directional multichannel system for scheduleduniform traffic of up to k concurrent transmissions from m sourcestations to n destination stations, all said source stations beingpartitioned into at least one source station group such that no morethan one said source station group contains less than k source stations,wherein k, m, n and p are positive non-zero integers and m≧k=( log_(p) nchoose (p-1)), said system comprising:a plurality p of transmitteroutputs in each said source station; a receiver input in each saiddestination station; and means for passively coupling optical signalsfrom said source stations to said destination stations such that thepower received at each said receiver input is greater than p/n² timesthe power transmitted from the respective said transmitter output..Iaddend. .Iadd.30. The shared directional multi-channel system of claim29, wherein said power received at said each receiver input is greaterthan (p/n/log_(p) n) times the power transmitted from said respectivetransmitter output. .Iaddend. .Iadd.31. A shared directionalmultichannel system for scheduled uniform traffic of up to k concurrenttransmissions from m source stations to n destination stations, all saidsource stations being partitioned into at least one source station groupsuch that no more than one said source station group contains less thank source stations, wherein k, m, n and p are positive non-zero integers,and m≧k= log₂ n , said system comprising: two transmitter outputs ineach said source station; a receiver input in each said destinationstation; and means for passively coupling optical signals from saidsource stations to said destination stations such that the powerreceived at each said receiver input is greater than 2/n² times thepower transmitted from the respective said transmitter output. .Iaddend..Iadd.32. The shared directional multi-channel system of claim 31,wherein said power received at said each receiver input is greater than(2/n/log₂ n) times the power transmitted from said respectivetransmitter output. .Iaddend.